The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting

We solve the Jang equation with respect to asymptotically hyperbolic "hyperboloidal" initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses on the case when the spatial dimension is equal to three.
Comment: 68 pages. Accepted by Commun. Math. Phys